How do I use dyntopo and mirror together?
You cannot effectively use the mirror modifier with dynamic typology (or sculpting in general, for that matter). 

Remove the modifier and then under the Dyntopo settings in a sculpt mode, ensure the "Direction" setting is correct and click "Symmetrize". You may get some pinching down the mirror axis, but this can be smoothed out manually.

After that, go to "Symmetry/Lock" in the same panel and select the correct mirror axis.